Multi-Robot Communication-Aware Cooperative Belief Space Planning with Inconsistent Beliefs: An Action-Consistent Approach

Multi-robot belief space planning (MR-BSP) is essential for reliable and safe autonomy. While planning, each robot maintains a belief over the state of the environment and reasons how the belief would evolve in the future for different candidate actions. Yet, existing MR-BSP works have a common assumption that the beliefs of different robots are consistent at planning time. Such an assumption is often highly unrealistic, as it requires prohibitively extensive and frequent communication capabilities. In practice, each robot may have a different belief about the state of the environment. Crucially, when the beliefs of different robots are inconsistent, state-of-the-art MR-BSP approaches could result in a lack of coordination between the robots, and in general, could yield dangerous, unsafe and sub-optimal decisions. In this paper, we tackle this crucial gap. We develop a novel decentralized algorithm that is guaranteed to find a consistent joint action. For a given robot, our algorithm reasons for action preferences about 1) its local information, 2) what it perceives about the reasoning of the other robot, and 3) what it perceives about the reasoning of itself perceived by the other robot. This algorithm finds a consistent joint action whenever these steps yield the same best joint action obtained by reasoning about action preferences; otherwise, it self-triggers communication between the robots. Experimental results show efficacy of our algorithm in comparison with two baseline algorithms.

Simplifying Complex Observation Models in Continuous POMDP Planning with Probabilistic Guarantees and Practice

Solving partially observable Markov decision processes (POMDPs) with high dimensional and continuous observations, such as camera images, is required for many real life robotics and planning problems. Recent researches suggested machine learned probabilistic models as observation models, but their use is currently too computationally expensive for online deployment. We deal with the question of what would be the implication of using simplified observation models for planning, while retaining formal guarantees on the quality of the solution. Our main contribution is a novel probabilistic bound based on a statistical total variation distance of the simplified model. We show that it bounds the theoretical POMDP value w.r.t. original model, from the empirical planned value with the simplified model, by generalizing recent results of particle-belief MDP concentration bounds. Our calculations can be separated into offline and online parts, and we arrive at formal guarantees without having to access the costly model at all during planning, which is also a novel result. Finally, we demonstrate in simulation how to integrate the bound into the routine of an existing continuous online POMDP solver.

No Compromise in Solution Quality: Speeding Up Belief-dependent Continuous POMDPs via Adaptive Multilevel Simplification

Continuous POMDPs with general belief-dependent rewards are notoriously difficult to solve online. In this paper, we present a complete provable theory of adaptive multilevel simplification for the setting of a given externally constructed belief tree and MCTS that constructs the belief tree on the fly using an exploration technique. Our theory allows to accelerate POMDP planning with belief-dependent rewards without any sacrifice in the quality of the obtained solution. We rigorously prove each theoretical claim in the proposed unified theory. Using the general theoretical results, we present three algorithms to accelerate continuous POMDP online planning with belief-dependent rewards. Our two algorithms, SITH-BSP and LAZY-SITH-BSP, can be utilized on top of any method that constructs a belief tree externally. The third algorithm, SITH-PFT, is an anytime MCTS method that permits to plug-in any exploration technique. All our methods are guaranteed to return exactly the same optimal action as their unsimplified equivalents. We replace the costly computation of information-theoretic rewards with novel adaptive upper and lower bounds which we derive in this paper, and are of independent interest. We show that they are easy to calculate and can be tightened by the demand of our algorithms. Our approach is general; namely, any bounds that monotonically converge to the reward can be easily plugged-in to achieve significant speedup without any loss in performance. Our theory and algorithms support the challenging setting of continuous states, actions, and observations. The beliefs can be parametric or general and represented by weighted particles. We demonstrate in simulation a significant speedup in planning compared to baseline approaches with guaranteed identical performance.

Online POMDP Planning with Anytime Deterministic Guarantees

Autonomous agents operating in real-world scenarios frequently encounter uncertainty and make decisions based on incomplete information. Planning under uncertainty can be mathematically formalized using partially observable Markov decision processes (POMDPs). However, finding an optimal plan for POMDPs can be computationally expensive and is feasible only for small tasks. In recent years, approximate algorithms, such as tree search and sample-based methodologies, have emerged as state-of-the-art POMDP solvers for larger problems. Despite their effectiveness, these algorithms offer only probabilistic and often asymptotic guarantees toward the optimal solution due to their dependence on sampling. To address these limitations, we derive a deterministic relationship between a simplified solution that is easier to obtain and the theoretically optimal one. First, we derive bounds for selecting a subset of the observations to branch from while computing a complete belief at each posterior node. Then, since a complete belief update may be computationally demanding, we extend the bounds to support reduction of both the state and the observation spaces. We demonstrate how our guarantees can be integrated with existing state-of-the-art solvers that sample a subset of states and observations. As a result, the returned solution holds deterministic bounds relative to the optimal policy. Lastly, we substantiate our findings with supporting experimental results.

Measurement Simplification in ρ-POMDP with Performance Guarantees

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible for many online systems. This paper introduces a novel approach to efficient decision-making, by partitioning the high-dimensional observation space. Using the partitioned observation space, we formulate analytical bounds on the expected information-theoretic reward, for general belief distributions. These bounds are then used to plan efficiently while keeping performance guarantees. We show that the bounds are adaptive, computationally efficient, and that they converge to the original solution. We extend the partitioning paradigm and present a hierarchy of partitioned spaces that allows greater efficiency in planning. We then propose a specific variant of these bounds for Gaussian beliefs and show a theoretical performance improvement of at least a factor of 4. Finally, we compare our novel method to other state of the art algorithms in active SLAM scenarios, in simulation and in real experiments. In both cases we show a significant speed-up in planning with performance guarantees.

Data Association Aware POMDP Planning with Hypothesis Pruning Performance Guarantees

Autonomous agents that operate in the real world must often deal with partial observability, which is commonly modeled as partially observable Markov decision processes (POMDPs). However, traditional POMDP models rely on the assumption of complete knowledge of the observation source, known as fully observable data association. To address this limitation, we propose a planning algorithm that maintains multiple data association hypotheses, represented as a belief mixture, where each component corresponds to a different data association hypothesis. However, this method can lead to an exponential growth in the number of hypotheses, resulting in significant computational overhead. To overcome this challenge, we introduce a pruning-based approach for planning with ambiguous data associations. Our key contribution is to derive bounds between the value function based on the complete set of hypotheses and the value function based on a pruned-subset of the hypotheses, enabling us to establish a trade-off between computational efficiency and performance. We demonstrate how these bounds can both be used to certify any pruning heuristic in retrospect and propose a novel approach to determine which hypotheses to prune in order to ensure a predefined limit on the loss. We evaluate our approach in simulated environments and demonstrate its efficacy in handling multi-modal belief hypotheses with ambiguous data associations.

Probabilistic Qualitative Localization and Mapping

Simultaneous localization and mapping (SLAM) are essential in numerous robotics applications, such as autonomous navigation. Traditional SLAM approaches infer the metric state of the robot along with a metric map of the environment. While existing algorithms exhibit good results, they are still sensitive to measurement noise, sensor quality, and data association and are still computationally expensive. Alternatively, some navigation and mapping missions can be achieved using only qualitative geometric information, an approach known as qualitative spatial reasoning (QSR). We contribute a novel probabilistic qualitative localization and mapping approach in this work. We infer both the qualitative map and the qualitative state of the camera poses (localization). For the first time, we also incorporate qualitative probabilistic constraints between camera poses (motion model), improving computation time and performance. Furthermore, we take advantage of qualitative inference properties to achieve very fast approximated algorithms with good performance. In addition, we show how to propagate probabilistic information between nodes in the qualitative map, which improves estimation performance and enables inference of unseen map nodes - an important building block for qualitative active planning. We also conduct a study that shows how well we can estimate unseen nodes. Our method particularly appeals to scenarios with few salient landmarks and low-quality sensors. We evaluate our approach in simulation and on a real-world dataset and show its superior performance and low complexity compared to the state-of-the-art. Our analysis also indicates good prospects for using qualitative navigation and planning in real-world scenarios.

Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints

Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings, calculating an optimal course of action inflicts an enormous computational burden on the agent. Moreover, in many scenarios, e.g., information gathering, it is required to introduce a belief-dependent constraint. Prompted by this demand, in this paper, we consider a recently introduced probabilistic belief-dependent constrained POMDP. We present a technique to adaptively accept or discard a candidate action sequence with respect to a probabilistic belief-dependent constraint, before expanding a complete set of future observations samples and without any loss in accuracy. Moreover, using our proposed framework, we contribute an adaptive method to find a maximal feasible return (e.g., information gain) in terms of Value at Risk for the candidate action sequence with substantial acceleration. On top of that, we introduce an adaptive simplification technique for a probabilistically constrained setting. Such an approach provably returns an identical-quality solution while dramatically accelerating online decision making. Our universal framework applies to any belief-dependent constrained continuous POMDP with parametric beliefs, as well as nonparametric beliefs represented by particles. In the context of an information-theoretic constraint, our presented framework stochastically quantifies if a cumulative information gain along the planning horizon is sufficiently significant (e.g. for, information gathering, active SLAM). We apply our method to active SLAM, a highly challenging problem of high dimensional Belief Space Planning. Extensive realistic simulations corroborate the superiority of our proposed ideas.

Monte Carlo Planning in Hybrid Belief POMDPs

Real-world problems often require reasoning about hybrid beliefs, over both discrete and continuous random variables. Yet, such a setting has hardly been investigated in the context of planning. Moreover, existing online Partially Observable Markov Decision Processes (POMDPs) solvers do not support hybrid beliefs directly. In particular, these solvers do not address the added computational burden due to an increasing number of hypotheses with the planning horizon, which can grow exponentially. As part of this work, we present a novel algorithm, Hybrid Belief Monte Carlo Planning (HB-MCP) that utilizes the Monte Carlo Tree Search (MCTS) algorithm to solve a POMDP while maintaining a hybrid belief. We illustrate how the upper confidence bound (UCB) exploration bonus can be leveraged to guide the growth of hypotheses trees alongside the belief trees. We then evaluate our approach in highly aliased simulated environments where unresolved data association leads to multi-modal belief hypotheses.

involve-MI: Informative Planning with High-Dimensional Non-Parametric Beliefs

One of the most complex tasks of decision making and planning is to gather information. This task becomes even more complex when the state is high-dimensional and its belief cannot be expressed with a parametric distribution. Although the state is high-dimensional, in many problems only a small fraction of it might be involved in transitioning the state and generating observations. We exploit this fact to calculate an information-theoretic expected reward, mutual information (MI), over a much lower-dimensional subset of the state, to improve efficiency and without sacrificing accuracy. A similar approach was used in previous works, yet specifically for Gaussian distributions, and we here extend it for general distributions. Moreover, we apply the dimensionality reduction for cases in which the new states are augmented to the previous, yet again without sacrificing accuracy. We then continue by developing an estimator for the MI which works in a Sequential Monte Carlo (SMC) manner, and avoids the reconstruction of future belief's surfaces. Finally, we show how this work is applied to the informative planning optimization problem. This work is then evaluated in a simulation of an active SLAM problem, where the improvement in both accuracy and timing is demonstrated.